You can put this solution on YOUR website! x^2-6x+8=0
x^2-6x=-8
Half of the middle term coefficient (6) is 3 so add square of 3 both sides of the equation.
x^2-6x+9=-8+9
x^-2(3)x+(3)^2=1
x^-2(3)x+(3)^2=1
(x-3)^2=1
x-3=1 or x-3=-1
x=1+3 or x=-1+3
x=4 or x=2
x^2+5x+6=0
x^2+5x=-6
Half of the middle term coefficient (5) is 5/2 so add square of 5/2 both sides of the equation.
x^2+5x+25/4=-6+25/4
x^2+2 (5/2)x+25/4=-6+25/4
x^2+2 (5/2)x+25/4=(-24+25)/4
x^2+2 (5/2)x+25/4=1/4
(x+5/2)^2=1/4
x+5/2=1/2 or x+5/2=-1/2
x=1/2-5/2 or x=-1/2-5/2
x=(1-5)/2 or x=(-1-5)/2
x=-4/2 or x=-6/2
x=-2 or x=-3
